## Freezing point depression

Freezing point depression FPDF or Anti Freezing Power AFP or Potere Anti-Congelante PAC is the lowering of the freezing point of water. When making ice cream this can be used to predict the softness or scoopability at a certain serving temperature. This is especially important in ice cream display cabinets where all the different flavored ice creams must have the same softness. The main ingredients that suppresses the freezing point is SUGAR, SALT and ALCOHOL. You have probably seen in many recipes that you can add a splash of alcohol or a little salt to make the ice cream softer. But the most important ingredient is sugar. By using different types of sugars you can control the sweetness and freezing point of your ice cream. If your ice cream is too hard but has the correct sweetness you can’t just add more sucrose to make it softer you have to use a mix of different sugars.

The freezing point depression in itself is a hint of how soft the ice cream will be, there are other factors to consider as well. If everything else is equal the ice cream with the highest PAC value will be softer. When we calculate the PAC in relation to the water content and look at the freezing curve we get a better measurement of softness.

## Science

The science behind freezing point depression is related to the molecular weight of an ingredient. Normal table sugar SUCROSE has a molecular weight of 342 and is used as a reference when calculating PAC. **100g of sucrose in 1000g of water has a PAC of 100**

Other types of sugars have different molecular weights and thus affects the freezing point differently. What we do is to calculate the **Sucrose Equivalent** of any other sugar.

## Implementation details

This section is an explanation of how PAC is implemented in the software. There is not a standard way of calculating this. Different sources calculate the PAC and FP in different ways and in different detail. My approach is like this. I calculate the PAC for sugars (PACse or PAC sucrose Equivalent) and use experimental data tables for sucrose solutions to calculate the FP. I then separately calculate the FP for salt, alcohol and for the salts in MSNF. These FPs are then added together to find the final FP. Alternative ways would be to sum the PAC from sugars, salts, alcohol and salts in MSNF to get one final PAC and either use the sucrose table to find the FP or use the linear formula for freezing point depression. So, if you look at other calculators or sources for PAC and freezing point calculations be aware that they might differ from my software both due to different calculations and also of course how the PAC is defined for the ingredients.

## Sugars

The most useful sugars in home ice cream making are sucrose, dextrose and fructose. These are all in powder form and is easy to measure and work with. Honey, glucose syrup and other syrups are also common. Lactose is the sugar in milk and also affects the freezing point.

Sugar | PAC | Relative sweetnessPOD |

Sucrose | 100 | 100 |

Dextrose | 190 | 70 |

Fructose | 190 | 170 |

Glucose syrup (DE42) | 80 | 50 |

Honey | 146 | 75 |

Lactose | 100 | 16 |

Salt* | 585 | 0 |

Alcohol* | 740 | 0 |

## Example

To illustrate assume we have the following ingredients.

Water 800g

Sucrose 200g*PAC 200POD 200*

The PAC will be 200 and the POD (relative sweetness) will also be 200. Now we want to keep the relative sweetness and raise the PAC. We can replace some of the sugar with dextrose to accomplish this. Since dextrose only have 70% sweetness compared to sucrose we also need to reduce the water to get the same sweetness.

Water 784g

Sucrose 162g

Dextrose 54g

*PAC 265*

POD 200

POD 200

So, by replacing some of the sucrose with dextrose we have kept the sweetness the same but increased the PAC making the ice cream softer.

If we use fructose as well we can use dextrose+fructose to get the same sweetness as sucrose.

Water 800g

Sucrose 150g

Dextrose 35g

Fructose 15g

*PAC 245*

POD 200

POD 200

So, we can use a blend of sugars to manipulate the sweetness and the freezing point depression of our ice cream.

## Freezing point

All water does not freeze at the same time. Using the PAC we can calculate when the water starts to freeze. This is called the freezing point or FP. So at the FP we have 0% frozen water. When water starts to freeze the concentration of the sugars increases resulting in a higher PAC for the remaining water. Thus we need lower temperatures to freeze more water and so on. This is also the reason why your ice cream machine can not freeze your ice cream completely.

To calculate the freezing point for sugars I use a table of experimental data of sucrose solutions. For salt and alcohol I use a linear formula based on the molality of salt and alcohol.

## Freezing curve

Adding the freezing point for the sugars, salt and alcohol we get the initial freezing point of the ice cream. By simulating more and more water being frozen we can plot a freezing curve. This curve can then be used to calculate the serving temperature of the ice cream or indicate how much water is frozen at a certain temperature. I try to aim for approx 75% frozen water at -14C.

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